How widely supported was Stanisław I Leszczyński in GD Lithuania?

Sep 2018
I do not know much about the War of the Polish Succession, so I'm hoping more knowledgeable people here can help me. When reading through the english Wikipedia article on Stanisław I Leszczyński, it claims that he was "elected king of Poland by an overwhelming majority of the Diet."
Stanisław Leszczyński - Wikipedia

I'd like to know, during the War of the Polish Succession, how much popular support in the Lithuanian part of the Commonwealth (including modern day Belarus and Ukraine) did Stanisław have? I know there were partisan forces fighting for him during the war; did any of them originate in the Grand Duchy?